Notes : each number refers to cubics with equations of the same type and with the same color in the table. Furthermore, Kxxxx(n+1) = X(1) x Kxxxx(n). Note that X(335) is the isotomic conjugate of X(239).

(1) : K323(n) = pK(X1^(2n+1), X1^n x X239)

(2) : K251(n) = pK(X1^(2n+1) x X239, X1^n)

(3) : K768(n) = pK(X1^(2n) x X335, X1^(n+1) x X335)

(4) : K769(n) = pK(X1^(2n+1) x X335, X1^n x X335)

(5) : K770(n) = pK(X1^(2n) x X239, X1^(n+1))

(6) : K132(n) = pK(X1^(2n+1), X1^n x X894)

(7) : K1002(n) = pK(X1^(2n), X1^n x X4645)

Remarks :

• these equations clearly show that the cubics above are weak for any n. It follows that the symbolic substitution SS{a -> a^2} transforms each cubic into a strong pK equivalent to K020 as in Table 66.